In you would like to be involved in reviewing books for this section, please send your contact details and area(s) of interest to the editor who will
forward books for review as and when they become available.
If you wish for a book to be reviewed, please send it to the editor who will arrange for it to be reviewed.
As we go to press, we learn that the ICMI Study History in Mathematics Education, launched last August at ICME-9 in Japan, is now available. Edited
by John Fauvel and Jan van Maanen, this 437 page book is published by Kluwer Academic Publishers as volume 6 of the 'New ICMI Studies', ISBN 0-7923-6399-X.
The history of this study is quite informative. Since the mid 1980s HPM's parent body, the International Commission on Mathematics Instruction, has
engaged in promoting a series of studies on essential topics and key issues in mathematics education, to provide an up-to-date presentation and analysis
of the state of the art in that area. By the early 1990s a consensus was growing that one of these studies should be devoted to the relations between
history and pedagogy of mathematics. Once ICMI Council agreed to this Study, which was announced at the Seville ICME in 1996, the current and immediate
past Chair of HPM, Jan van Maanen and John Fauvel, were approached to chair the Study. ICMI's support for and promotion of this Study can thus be seen as
recognition of how the HPM Study Group had encouraged and reflected a climate of greater international interest in the value of history of mathematics for
mathematics educators, teachers and learners.† Concerns throughout the international mathematics education community had begun to focus on such
issues as the many different ways in which history of mathematics might be useful, on scientific studies of its effectiveness as a classroom resource,
and on the political process of spreading awareness of these benefits through curriculum objectives and design. It was judged that an ICMI Study would be a
good way of bringing discussions of these issues together and broadcasting the results, with benefits, it is to be hoped, to mathematics instruction
worldwide.
ICMI Studies typically fall into three parts: a widely distributed Discussion Document to identify the key issues and themes of the study; a Study
Conference where the issues are discussed in greater depth; and a Study Volume bringing together the work of the Study so as to make a permanent
contribution to the field.
The Discussion Document was drawn up by the two people invited by ICMI to co-chair the Study, John Fauvel (Open University, UK; HPM chair 1992-1996)
and Jan van Maanen (University of Groningen, Netherlands; HPM chair 1996-2000), with the assistance of the leading scholars who formed the
International Programme Committee: Abraham Arcavi (Israel), Evelyne Barbin (France), Jean-Luc Dorier (France), Florence Fasanelli (US, HPM Chair
1998-1992), Alejandro Garciadiego (Mexico), Ewa Lakoma (Poland), Mogens Niss (Denmark) and Man-Keung Siu (Hong Kong). The Discussion Document was widely
published, and was translated into several other languages including French, Greek and Italian. From the responses and from other contacts, some eighty
scholars were invited to a Study Conference in the spring of 1998, an invitation which in the event between sixty and seventy were able to accept.
The Study Conference took place in the south of France, at the splendid country retreat of the French Mathematical Society, CIRM Luminy (near
Marseille), from 20 to 25 April 1998. Local organisation was in the hands of Jean-Luc Dorier (University of Grenoble). The scholars attending were from a
variety of backgrounds: mathematics educators, teachers, mathematicians, historians of mathematics, educational administrators and others. This rich
mix of skills and experiences enabled many fruitful dialogues and contributions to the developing study.
The means by which the Study was advanced, through the mechanism of the Conference, is worth description and comment. Most participants in the
Conference had submitted papers, either freshly written or recent position papers, for the others to read and discuss, and several studies were made
available by scholars not able to attend the meeting. These, together with whatever personal qualities and experiences each participant was bringing to
the Conference, formed the basis for the work. Apart from a number of plenary and special sessions, the bulk of the Conference's work was done through
eleven working groups, corresponding, in the event, to the eleven chapters of the Study Volume. Each participant belonged to two groups, one meeting in the
mornings and one in the afternoons. Each group was led by a convenor, responsible for co-ordinating the group's activities and playing a major part
in the editorial activity leading to the eventual chapters of the book. Each group's work continued for several months after the Conference, with almost
everyone participating fully in writing, critical reading, bibliographical and other editorial activities.
This way of group working for a sustained period towards the production of a book chapter was a fresh experience to many participants, since the pattern
of individual responsibility for separate papers is a more common feature of such meetings and book productions. In this instance the participants proved
remarkably adept at using the new structures to come up with valuable contributions to the development of the field, all the more valuable for
their being the results of consensual discussions and hard-written contributions, which were then edited and designed into the Study Book.
In the end the Study Book was a xviii + 437 page volume, with some 62 contributors, working together in eleven teams. The chapter titles and team
leaders are as follows:
We hope that HPM members will be able to encourage their institutional libraries to order the book! The institutional price is 185US$. For
individual HPM members, a much-reduced special price is available through ICMI. Details of that will follow in the next HPM Newsletter.
Wasan is the mathematics developed in Japan during the Edo period (1603 -- 1867). Jinkoki, a book of mathematics in a very early stage of Wasan and the
most popular textbook of mathematics during the Edo period, is translated into English and published by Wasan Institute, Tokyo, Japan. It is the first
English translation of an entire text of a book of Wasan. The Institute also published a present-day Japanese version of Jinkoki.
Jinkoki was written by Yoshida Mitsuyoshi (Yoshida is the family name) and the first edition was published in 1627. He revised it several times. It was
a book of mathematics for ordinary people: merchants, carpenters and so on. Elements of mathematics, which would be useful for their daily lives, were
treated by examples.
After Jinkoki, many others made similar publications, and many people learned elementary mathematics by such books during the Edo period.
The original text for English translation is the 1641 June edition, as it has the most complete style. The contents of the English translation of Jinkoki
are as follows:
For further information and copies, contact Wasan Institute, 5-14-9-108 Sakurajousui,Setagaya-ku, Tokyo 156-0045 JAPAN
The first thing you see on the cover is Cardano's face looking towards the three title words. We have missed this book in France! The part of our math
course on complex numbers, studied by the scientific "Terminale" classes (17/18 year olds)) generally gives us the unique opportunity to ask questions
like: "Who did invent numbers? What is actually a number? What are they made for?" Original texts by Cardano and Bombelli have been available here for 40
years. Introducing complex numbers by using historical ways is not rare, but we missed the opportunity to reflect on it.
This is not just another book on history of mathematics, since it also contains other points of view. In particular, high school teachers write
about their own experiments in the classroom and also dare to write about philosophical matters! For instance, Anne Boy´'s chapter contains excerpts
from Cardano's and Tartaglia's books amongst others, but it doesn't begin with them. She thinks introducing i too quickly is not suitable for pupils,
so she comes very slowly to the Italian solution of equations of the third degree, after having justified the interest of such a solution by quoting
constructions of polygons (The enneagon, how many sides?). At the other side of the process, the slow assimilation of imaginary "numbers" to the status of
complex numbers is a fascinating episode.
Maryvonne Hallez and Odile Kouteynikoff focus on the latter point, in its geometrical aspect of the settlement of complex numbers, quoting authors such
as Carnot and Argand, as well as the ghost of Kant. Many extracts from original texts remind us of the long time of maturation and the scientists' hesitations in the eighteenth century (It brings us together with our
pupils...). But if imaginary numbers are very useful for problem solving, they also form a "new" set, whose properties can be studied for themselves: G´rard
Hamon points out the structural dimension (Galois, Hamilton as well as Cardan, Bombelli and Euler.).
But that's not all! Different historical perspectives proposed in action for introducing complex numbers (subtitle of this book) are surrounded by
historical and philosophical chapters. The book leads us to think about the links between classroom and epistemological research. Some chapters could
hardly be used with pupils, but it is very interesting to read them for themselves. Jean-Luc Verley's first chapter sketches the "complex" history of
complex numbers. Jean-Pierre Friedelmeyer sheds light upon the Gauss proof of the fundamental theorem of algebra, showing that this particular proof has
dispelled the mist in which the numbers lay. Friedelmeyer stresses on the link to vectors and the relationship between physics and complex numbers: it
is amazing to realise how a purely abstract theory gives information about nature and allows us to understand it in a new way.
This aspect of the problem is treated by Maurice Thirion: what is the link between imaginary numbers and reality? Thirion is one of this book's
philosophers, the other ones are Marie José Durand-Richard and Jean-Pierre Clévero, who has written the postscript. Why were complex numbers so
fascinating and why did their inventors hesitate so much? The reflection is not so understandable to the ordinary math teacher.
But this is why Images, imaginaires, imagination will be your pillow book (if only you read French!) for a long time. Don't you call that interactivity?
Frédéric Metin, Dijon IREM
Pp.165 Malaysian ringgit RM40 (£7 plus £2 postage) 20000.ISBN 510.92217671 (To order write a cheque or charge to Bendahari UTM and send FAO Yosman bin Mohd Bain, Penerbit UTM, Universiti Teknologi Malaysia, 81310 Skudai, Johor, Malaysia e-mail Yosman@mel.utm.my
On the back of this book the author says "This book presents detailed accounts and analyses of the lives and world view of selected mathematicians of the Islamic period, their place in the world of science, the popularisation of their lives, and their contributions specifically in mathematics and astronomy. The mathematicians whose lives and works are elaborated in this book are al-Khwarizmi, Ibn al-Haytham, al-Biruni, Omar Khayyam and al-Tusi. This book negates the unjustified views made by some historians that the Muslims did not make any original contribution to mathematics and that they were mere preservers of knowledge of the Greeks. Numerous new documents have been discovered and old documents have been reread with a more critical and understanding mind. The results confirmed the fact that the contributions of mathematicians of the Islamic period indeed were of prime importance and greatly affected the development of all branches of modern mathematics. This book can be used as a reference for students in the field of history of mathematics and is also appropriate for mathematics students, teachers and instructors as well as for anyone in related fields."
I thoroughly agreed with this description. I found it a fascinating book to read, having met little in this area. It makes a substantial contribution to books on the debt we owe Islamic civilisation to mathematics. Mohaini Mohamed has written a very readable book that is well worth acquiring by anybody who is interested in mathematics and its history. It should find its place into every library from school to university.
Peter Ransom, The Mountbatten School
This section contains references to books or articles that may be of interest to all those concerned with the history of mathematics. Please send details with complete bibliographic information to the editor for inclusion in future issues.
Bagheri, Mohammad, Recreational Problems from Hasib Tabariís Miftah al-Muamalat, Ganita Bharati, Bull. Ind. Soc. Hist. Math, Vol.21, Nos 1-4 (1999), 1-9.
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